Consistent adaptive sequential dictionary learning

Abstract

Algorithms for learning overcomplete dictionaries for sparse signal representation are mostly iterative minimization methods that alternate between a sparse coding stage and a dictionary update stage. For most however, the notion of consistency of the learned quantities has not been addressed. Based on the observation that the observed signals can be approximated as a sum of rank one matrices, a new adaptive dictionary learning algorithm is proposed in this paper. It is derived via sequential adaptive penalized rank one matrix approximation where the ℓ1-norm is introduced as a penalty promoting sparsity. The proposed algorithm uses a block coordinate descent approach to consistently estimate..